
838 THE AMERICAN NATURALIST.  [Vor. XXXVI. 
angles,” not only among fishes of different groups but between 
fishes and cetaceans; for in these practically the same “ lines " 
and “entering angles ” ! obtain. 
From a physical standpoint we conclude, therefore, that the 
position of the gravity center of the animal during different 
stages of growth plays an important róle in connection with its 
ever-increasing body length, and that special organs of balancing, 
t.e., fins, will in their development be subject par excellence to 
the mechanical needs in shifting which the changing position 
of the gravity center and increasing body length demand. 
From this standpoint, then, one can attack the long-troubled 
problem of the origin of the vertebrate limbs. Not, however, 
with the aim of solving it indisputably, — for this I firmly 
believe can be done only by the paleontologist, — but rather 
for the purpose of finding a probable clue to the labyrinthine 
confusion in latest morphological studies ; for the voluminous 
conclusions of Braus, following Gegenbaurian teachings, and 
supported by Semon in his recent work on Ceratodus, — cf. 
also the related work of Klaatsch, — are vigorously denied by 
the newer phases of the fin-fold theory of Dohrn, Mollier, 
Rabl, and others, which in turn are in the latest time criticised 
by Fürbringer. In short, there is at present a deadlock in the 
discussion as to the mode of origin of the limbs of the verte- 
brates which cannot yet be loosened by orthodox embryological 
methods. Perhaps it will be bettered when a greater number 
of forms will have been examined, or when we shall have a 
clearer knowledge of the processes of accelerated and retarded 
development. Perhaps, on the other hand, to take a more 
somber view, it will never be adequately loosened by study of 
embryonic structures, since these may have been so modified 
during phylogeny as to mask hopelessly their true homologies. 
For the discussion has to a large measure narrowed itself down 
to the interpretation of embryological details, which if given 
fixed morphological weight become of great importance in 
theoretical discussion, but which are relatively valueless if 

! The entering angle terminates with * wonderful uniformity" at 36 per cent 
of the total length of the animal, whether teleost or cetacean. Cf. especially 
H. DeB. Parsons, Trans. Amer. Soc. Engineers, vol. ix, penn 17 pp» 7 pls. 
